By taking its point of departure as a concern for the way students actually use tools and symbols, and for what these signify for them, this book explores the option of building on symbolizing, modelling and tool use as personally meaningful activities of students.

and overview.- Preamble: from models to modeling.- Section I: Emergent modeling.- to section I: Informal representations and their improvements.- The mathematization of young children’s language.- Symbolizing space into being.- Mathematical representations as systems of notations-in-use.- Students’ Criteria for Representational Adequacy.- Transitions in emergent modeling.- Section II: The role of Models, Symbols and Tools in instructional design.- to section II: The role of Models, Symbols and Tools in instructional design.- Emergent models as an instructional design heuristic.- Modeling, Symbolizing, and Tool Use in Statistical Data Analysis.- Didactic objects and didactic models in radical constructivism.- Taking into account different views: Three brief comments on papers by Gravemeijer & Stephan, Cobb and Thompson.- Section III: Models, situated practices, and generalization.- to section III: Models, situated practices, and generalization.- On Guessing the Essential Thing.- Everyday knowledge and mathematical modeling of school word problems.- On the development of human representional competence from and evolutionary point of view: From Episodic To Virtual Culture.- Modeling Reasoning.